Children Like Patterns Too

This series of designs derived from a children's board game.
It comprises of square pieces of card on which are drawn various coloured lines - the object of the game being to connect the lines such that continuous loops are formed.
This intrigued me in that I wondered if it was possible to derive a pattern using just one of the pieces duplicated dozens of times.
I chose the square shown in Figure 1 and though I succeeded in generating a number of patterns, none of them interested me much - the format was just too limiting.
However when I used two different pieces (Figure 1 and Figure 2) a number of more complex patterns emerged, one of which is seen at Figure 3.
It was then just a matter of adding colour (Figure 4) and finally, with the help of CorelDraw's Extrude tool some 3-dimensionality (Figure 5).
There are of course many patterns that can be derived using this principle. In some I have tried to maintain symmetry around both diagonals and in others formed a continuous woven loop around the whole grid. I have found it difficult to achieve both simultaneously - my best effort to date is at Figure 6.
I've recently discovered a number of other games based on the same idea - I found one in France recently called Tantrix, but in this instance the tiles are hexagonal in shape. I haven't yet played with this idea using hexagons, but on one quiet winters day I might just get round to it.
Please feel free to pre-empt me.
Of course once you start down this path the permutations are endless. I haven't even begun to try using more than one colour or combinations of shapes (imagine trying this with Roger Penrose's non-repeating space-filling patterns).
My thanks go out to GALT without whose Connect game I wouldn't have had so much fun.


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